Primality proof for n = 5396885861:
Take b = 2.
b^(n-1) mod n = 1.
7293089 is prime. b^((n-1)/7293089)-1 mod n = 1317483561, which is a unit, inverse 3345450373.
(7293089) divides n-1.
(7293089)^2 > n.
n is prime by Pocklington's theorem.